MOSCOW, Dec 8 (Reuters) - The U.S. Senate's passage of legislation to punish Russians who violate human rights is the first big test of the resolve of Vladimir Putin and Barack Obama to improve relations since their election victories.

Obama, who launched a "reset" in relations with Russia less than four years ago, is likely to sign the law even though Moscow sees it as "aggressively unfriendly." Damage to U.S.-Russian relations is all but inevitable.

But there are signs that Putin, who won the presidency despite the biggest protests of his 13-year rule, may want to put the bad blood of a campaign in which he whipped up anti-American sentiment behind him.

"I do not think that this will lead to a serious crisis in Russian-American relations," said Dmitry Trenin, director of the Carnegie Moscow Centre think tank.

"(Putin) does not intend to make relations worse, and for this reason the effects of this legislation will be limited," Trenin said.

The Senate approved the "Magnitsky Act" as part of a broader bill to lift a Cold War-era restriction and grant Russia "permanent normal trade relations, " or PNTR, a move that in other circumstances would have been celebrated in both capitals.

A month after Obama's re-election, it could have been the cap on a period during which he signed a landmark nuclear arms deal with Moscow and helped usher Russia into the World Trade Organization after an 18-year membership bid.

Instead, Moscow is furious over the human rights portion of the bill, an unmistakable message to Putin of displeasure with the treatment of Russians who dare challenge the authorities.

The main targets are those allegedly involved in the abuse and death of Sergei Magnitsky, a lawyer who died in jail in 2009 - the victim, colleagues say, of retribution from the same investigators he claimed stole $230 million from the state.

In a Foreign Ministry statement full of righteous anger, Russia called the Senate vote a "performance in the theatre of the absurd" and said the bill would badly cloud the prospects for cooperation between Moscow and Washington.

How big the impact will be is largely up to Putin.

The law injects a dose of poison into a relationship strained by the crisis in Syria and U.S. concerns about the direction Putin has taken since he revealed last year that he would return to the Kremlin after a stint as prime minister.

"It will have a negative impact on the atmosphere, that's for sure," said Samuel Charap, senior fellow for Russia and Eurasia at the International Institute for Strategic Studies in Washington.

The bill directs Obama to publish the names of Russians allegedly involved in the abuse and death of Magnitsky, who was jailed in 2008 on tax evasion and fraud charges colleagues say were fabricated by investigators against whom he had given evidence.

Magnitsky, 37, said he was deliberately deprived of the treatment he needed as his health deteriorated painfully in jail, and the Kremlin's own human rights council has said he was probably beaten to death.

The bill would also require the United States to deny visas and freeze the assets of any of those individuals, as well as other human rights violators in Russia not linked to Magnitsky, on a continuing basis.

It is, at least in Russian eyes, almost a textbook example of what Putin dislikes most about the United States: its perceived use of human rights concerns as a geopolitical instrument and the resort to sanctions for punishment.

In a decree signed hours after his inauguration to a six-year third term in May, Putin said he wanted "truly strategic" ties with the United States but they must be based on equality, non-interference and respect for one another's interests.

MUTUAL DOUBTS

Trenin said the law would reinforce Putin's wariness about U.S. intentions, but that he may also want to focus on his long-stated goal of improving economic ties with the United States.

Russia has sought to reassure Americans that Moscow's response to the bill would not affect business dealings.

But late on Friday, Russia imposed restrictions on meat imports from several countries, chief among them the United States, denying the move was a political retribution for the "Magnitsky Act".

In a joint statement on Saturday, U.S. Trade Representative Ron Kirk and Agriculture Secretary Tom Vilsack said Russia's new requirement for imported beef and pork to be certified free of ractopamine, a feed additive used in the U.S. meat industry but banned in some other countries, appeared to be a violation of Moscow's WTO obligations.

"The United States calls on Russia to suspend these new measures and restore market access for U.S. beef and pork products," Kirk and Vilsack said.

"The United States sought, and Russia committed as part of its WTO accession package, to ensure that it adhere rigorously to WTO requirements and that it would use international (food safety) standards unless it had a risk assessment to justify use of a more stringent standard," they said.

On Saturday, the daily Kommersant reported that the passage of the legislation may freeze the work of some of the 20-plus groups that are part of the bilateral presidential commission set up between Obama and former President Dmitry Medvedev.

The Magnitsky Act is the flip side of the bill to grant Russia PNTR status, which both sides hope, along with Russia's WTO membership, will bolster bilateral trade, which amounted to a paltry $43 billion last year.

"There's a lot that can be done on that, and that is stuff he understands and cares about," Charap said of Putin.

Russia has threatened to retaliate if Obama signs the bill into law. Foreign Minister Sergei Lavrov told U.S. Secretary of State Hillary Clinton on Thursday that Russia would bar entry for Americans "guilty of crude human rights abuses."

Moscow has also warned it would respond with "asymmetrical" measures, seeming to hint the bill could have a spillover effect into broader areas in which the United States wants Russian cooperation most, such as nuclear arms control and Iran.

But analysts said that was unlikely. They said the law would probably not derail Russian assistance on Afghanistan, or affect diplomacy aimed to curb Iran's nuclear programme or deepen disputes over U.S. missile defence and the conflict in Syria.

"It will have a mostly symbolic effect," said Yevgeny Volk, a Russian political analyst.